2. A particle moves according to the equation `x = 10t^2`, where `x` is in meters and `t` is in seconds.
(a) Find the average velocity for the time interval from `2.00 s` to `3.00 s`.
(b) Find the average velocity for the time interval from `2.00 s` to `2.10 s`.
`overline(v) = (∆x)/(∆t)`
(a) `50.0 m//s`
(b) `41.0 m//s`
Given: `x = 10t^2` or
(a)
`x_((2)) = 10times(2.00)^2 = 40.0 m`
`x_((3)) = 10times(3.00)^2 = 90.0 m`
`overline(v) = (90 m - 40 m)/(3.00s - 2.00s) = color(red)(50.0 m//s)`
(b)
`x_((2)) = 10times(2.00)^2 = 40.0 m`
`x_((2.1)) = 10times(2.10)^2 = 44.1 m`
`overline(v) = (44.1 m - 40 m)/(2.10s - 2.00s) = color(red)(41.0.0 m//s)`
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